A New Progressive Radial Basis Function Network Method to Interpolate a Regional Variable in Geosciences

Various interpolation and estimation tools are used to spatially model a regional variable across an area or site. This paper presents a new interpolation method, using the progressive radial basis function network and taking into account the spatial coordinates of the input data. The procedure starts with the study of the spatial structure and anisotropy of the data, to perform interpolation and determining the radiuses and rotation angles based on the directional variography. Next, the neighborhood radius and neighboring points of each node of hidden unit are determined, using the ellipsoidal anisotropy and the covariance matrix. Then, a shape factor is computed based on half the average distance of all the neighboring sample points. The progressive kernel matrix includes the corrected kernel functions and the coordinates of the nodes in the hidden units utilized to solve the weight matrix. The interpolation was finally performed at each point of regular network (unsampled points). The steps of this interpolation algorithm were evaluated by a synthetic data set, having an irregular 3D pattern. The Cross validation between actual and estimated values have a correlation coefficient of about 0.78 and the fitted line passing through the actual and estimated values is close to 45 degrees.